What’s 20 Divided by 7 as a Mixed Fraction?

What’s 20 Divided by 7 as a Mixed Fraction?

To express 20 divided by 7 as a mixed fraction, first perform the division:

20 ÷ 7 = 2 with a remainder of 6.

So, the quotient is 2, and the remainder is 6. To convert this into a mixed fraction, write it as:

2 6/7.

Therefore, 20 divided by 7 as a mixed fraction is 2 6/7.

Dividing Whole Numbers to Make Mixed Fractions

Dividing two whole numbers can often result in a fractional quotient. Mixed fractions contain both a whole number and a fraction joined together. Converting a division result to a mixed fraction is a useful skill for expressing remainders properly and identifying the fractional part of a quotient.

Let’s walk through dividing 20 by 7 and representing it as a mixed fraction.

Dividing Using Long Division

We’ll first divide using the standard long division algorithm:

20 / 7 = 2 R 6

So 20 divided by 7 equals 2 with a remainder of 6.

Converting to a Mixed Fraction

To convert the remainder to a fraction, we make it the numerator over the divisor (7) as the denominator:

R 6/7

Now we can combine it with the whole number quotient to make a mixed fraction:

2 (whole number quotient) 6/7 (remainder fraction)

So 20/7 expressed as a mixed fraction is 2 6/7.

Visualizing the Result

We can visualize this result on a number line:

If we divide 20 into 7 equal sections of size 7,

• 2 full sections give us the whole number portion
• 6/7 of the last section gives us the remainder fraction

Checking the Work

To verify the mixed fraction is correct, we can multiply it by 7 to see if it equals 20:

2 6/7 * 7 = 14 + 6 = 20 ✅

Getting back 20 confirms that 20/7 = 2 6/7 when expressed in mixed fraction form.

Converting division results into mixed fractions provides the most complete form of the quotient. This builds fluency with fractions as numbers and visualizing division as splitting into equal parts.

In summary, to express a whole number division result as a mixed fraction, make the remainder the numerator over the divisor as the denominator, and combine it with the whole number quotient.